Page 121 - Dynamic Loading and Design of Structures

Page 98

crosses a curving, steep sided valley, and the inference from its behaviour in service is that the
resulting disturbance might have presented serious response, even in the absence of
supplementary damping (Wex and Brown, 1981).
Although solid parapets are strongly adverse, porous windshielding barriers have only
moderate adverse effect. The initial feasibility study for the Second Severn Crossing
suggested that with full length 3 m/50 per cent solidity windshielding, a full ‘streamlined’
enclosure of the girder structure would be necessary to reduce excitation. In the event,
satisfactory performance has been achieved by painstaking wind tunnel optimization of the
edge detail supplemented by two non-structural longitudinal dividers below the deck. The
2
criterion for this design was an acceleration amplitude limit of 0.2n −1/2 m/s (actual n=0.33
Hz).

3.3 AEROELASTIC EXCITATION

3.3.1 The quasi-steady model: galloping
The concept of change in aerodynamic forces in response to the vector resultant relative
velocity has already been introduced, with respect to aerodynamic damping, in Section 3.1.5.
There are, however, circumstances in which aerodynamic damping becomes negative. If the
net damping (algebraic sum of structural and aerodynamic components) becomes negative, a
harmonic response at the natural frequency will develop. Unless structural failure (or
enhanced damping due to inelastic behaviour at large amplitudes) intervenes, the amplitude
reached will be limited by non-linearity of the force coefficient relationship to amplitude, but
such amplitudes may be very large. The classic example is the overhead line with ice
accretion, in which amplitudes of several metres have occurred on cables of a few centimetres
diameter, commonly appearing as travelling waves and giving the phenomenon of the generic
name ‘galloping’.
The basic linear quasi-steady model is shown in Figure 3.6(a), which postulates the form of
variation of lift force coefficient with angle of incidence that is shown by rectangular prisms
(i.e. negative over a range of incidence close to in-line with the longer side, as shown).
A perpendicular motion downwards as drawn, causing the relative incidence vector to be
inclined upwards, will thus result in a change of lift tending to reinforce the motion. For the
case shown, the downward velocity is . The apparent angle of incidence is
thus . For small values of a, writing and , this becomes

and the body axis force per unit length of the prism is

(3.47)

in which C and C are the coefficients for lift and drag forces as shown, referred to reference
L
D
dimension D. It will be seen that the positive direction for Z opposes